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POPULAR SCIENCE REVIEW. 
opposition to preconceived ideas,” lie u considers that the enormously in- 
creased ratio with which the numbers of the telescopic stars are multiplied 
is deserving of increased interest and continued discussion.” A very brief 
study of Mr. Proctor’s chart projection of Argelander’s Durchmusterung 
shows that Mr. Plummer’s conclusion, though not correct for the star-sphere 
as a wffiole, corresponds with what is observed over the region of the Milky 
Way. 
Two new Inequalities in the Moons Longitude. — In June 1876, a corre- 
spondent of the u English Mechanic ” pointed out, over the signature 
u W r . G. P.,” two theoretical inequalities in the moon’s longitude which 
had not hitherto been noticed, suggesting that they may possibly explain 
some actual inequalities observed in the moon’s motion. “ Some years ago I 
found,” he wrote, on June 30, p. 405, vol. xxiii. of the “English Mechanic,” 
“ that there were two inequalities, due partly to the direct and partly to 
the indirect action of Jupiter; the one of which agrees very exactly in 
period, and the other very fairly so” with those mentioned . . . They 
are : — 
— sin {(2 — 27— c)t — 2e fa} 
where i represents the mean motion of Jupiter, that of the moon being 
unity, and *006306 being taken for that of i; also e and a are the mean 
longitude of Jupiter and of moon's perigee when t = 0. “ The period of the 
above is very nearly 27*434 days, which falls within the narrow limits 
27*42 and 27*44, given by observation. It remains to be seen whether, 
besides this, 1" represents pretty well the proper amount of the inequality at 
its maximum, and whether a maximum occurs at the proper time. With 
regard to the long inequality, it will be of the form — 
p sin {(2 — 2/— 2n)t — 2e + 2a] 
its period will be about 17£ years. That of the observed is given at 
16§ years, with a probable error of half a year; and therefore with a 
possible error of eight months this would make it within the period of the 
calculated inequality.” In later numbers these inequalities were discussed 
by “ W. G. P.” and by another skilful mathematician, W. C. Evans, who 
analysed their value, describing fully his method of procedure, and in par- 
ticular explaining carefully, for a third correspondent, “ N.” (understood to 
have been Mr. Neison), certain difficulties under which “ N.” laboured. 
Nine months later these identical inequalities were submitted to the Astro- 
nomical Society by Mr. Neison, and so far claimed as his, that in a paper 
which appeared in the June number of the “ Monthly Notices,” Professor 
Newcomb, unaware of their prior discussion by “ W. G. P.” and Mr. Evans, 
speaks of them as “ new inequalities in the moon’s longitude pointed out 
by Mr. Neison.” We would suggest to Mr. Neison’s consideration that his 
procedure in this matter has been ill-considered. He has, we will assume, 
been able, directed as he was by the two mathematicians referred to, to re- 
calculate these inequalities, with closer approximation to their true value. 
Whatever credit may be due to him on this account would gladly have 
been accorded ; the credit of noticing the inequalities he should not have 
claimed, for it is not his. 
